Pregunta
Select your answer Simplify \( \sec \left(\frac{2 \pi}{3}\right) \) \( -\infty \) -2 2
Ask by Cox Gross. in the United States
Feb 28,2025
Solución de inteligencia artificial de Upstudy
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The value is -2.
Solución
Calculate or simplify the expression \( \sec\left(\frac{2\pi}{3}\right) \).
Calculate the value by following steps:
- step0: Calculate:
\(\sec\left(\frac{2\pi }{3}\right)\)
- step1: Rewrite the expression:
\(-\sec\left(\frac{\pi }{3}\right)\)
- step2: Calculate:
\(-2\)
The value of \( \sec\left(\frac{2\pi}{3}\right) \) is -2.
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Simplifique esta solución Beyond the Answer
To simplify \( \sec \left(\frac{2 \pi}{3}\right) \), we first express secant in terms of cosine: \( \sec(x) = \frac{1}{\cos(x)} \). The angle \( \frac{2 \pi}{3} \) is in the second quadrant, where cosine is negative. In fact, \( \cos\left(\frac{2 \pi}{3}\right) = -\frac{1}{2} \). Therefore, \( \sec\left(\frac{2 \pi}{3}\right) = \frac{1}{-\frac{1}{2}} = -2 \). The answer is \( -2 \). So, the correct answer is \( -2 \).
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